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EmpiricalDistribution (Commons Math 3.2 API)
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org.apache.commons.math3.random</FONT>
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Class EmpiricalDistribution</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">org.apache.commons.math3.distribution.AbstractRealDistribution</A>
      <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.random.EmpiricalDistribution</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</A>, <A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</A></DD>
</DL>
<HR>
<DL>
<DT><PRE>public class <B>EmpiricalDistribution</B><DT>extends <A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</A></DL>
</PRE>

<P>
<p>Represents an <a href="http://http://en.wikipedia.org/wiki/Empirical_distribution_function">
 empirical probability distribution</a> -- a probability distribution derived
 from observed data without making any assumptions about the functional form
 of the population distribution that the data come from.</p>

 <p>An <code>EmpiricalDistribution</code> maintains data structures, called
 <i>distribution digests</i>, that describe empirical distributions and
 support the following operations: <ul>
 <li>loading the distribution from a file of observed data values</li>
 <li>dividing the input data into "bin ranges" and reporting bin frequency
     counts (data for histogram)</li>
 <li>reporting univariate statistics describing the full set of data values
     as well as the observations within each bin</li>
 <li>generating random values from the distribution</li>
 </ul>
 Applications can use <code>EmpiricalDistribution</code> to build grouped
 frequency histograms representing the input data or to generate random values
 "like" those in the input file -- i.e., the values generated will follow the
 distribution of the values in the file.</p>

 <p>The implementation uses what amounts to the
 <a href="http://nedwww.ipac.caltech.edu/level5/March02/Silverman/Silver2_6.html">
 Variable Kernel Method</a> with Gaussian smoothing:<p>
 <strong>Digesting the input file</strong>
 <ol><li>Pass the file once to compute min and max.</li>
 <li>Divide the range from min-max into <code>binCount</code> "bins."</li>
 <li>Pass the data file again, computing bin counts and univariate
     statistics (mean, std dev.) for each of the bins </li>
 <li>Divide the interval (0,1) into subintervals associated with the bins,
     with the length of a bin's subinterval proportional to its count.</li></ol>
 <strong>Generating random values from the distribution</strong><ol>
 <li>Generate a uniformly distributed value in (0,1) </li>
 <li>Select the subinterval to which the value belongs.
 <li>Generate a random Gaussian value with mean = mean of the associated
     bin and std dev = std dev of associated bin.</li></ol></p>

 <p>EmpiricalDistribution implements the <A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution"><CODE>RealDistribution</CODE></A> interface
 as follows.  Given x within the range of values in the dataset, let B
 be the bin containing x and let K be the within-bin kernel for B.  Let P(B-)
 be the sum of the probabilities of the bins below B and let K(B) be the
 mass of B under K (i.e., the integral of the kernel density over B).  Then
 set P(X < x) = P(B-) + P(B) * K(x) / K(B) where K(x) is the kernel distribution
 evaluated at x. This results in a cdf that matches the grouped frequency
 distribution at the bin endpoints and interpolates within bins using
 within-bin kernels.</p>

<strong>USAGE NOTES:</strong><ul>
<li>The <code>binCount</code> is set by default to 1000.  A good rule of thumb
    is to set the bin count to approximately the length of the input file divided
    by 10. </li>
<li>The input file <i>must</i> be a plain text file containing one valid numeric
    entry per line.</li>
 </ul></p>
<P>

<P>
<DL>
<DT><B>Version:</B></DT>
  <DD>$Id: EmpiricalDistribution.java 1457372 2013-03-17 04:28:04Z psteitz $</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../serialized-form.html#org.apache.commons.math3.random.EmpiricalDistribution">Serialized Form</A></DL>
<HR>

<P>
<!-- =========== FIELD SUMMARY =========== -->

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<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Field Summary</B></FONT></TH>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#DEFAULT_BIN_COUNT">DEFAULT_BIN_COUNT</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Default bin count</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;<A HREF="../../../../../org/apache/commons/math3/random/RandomDataGenerator.html" title="class in org.apache.commons.math3.random">RandomDataGenerator</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#randomData">randomData</A></B></CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;RandomDataGenerator instance to use in repeated calls to getNext()</TD>
</TR>
</TABLE>
&nbsp;<A NAME="fields_inherited_from_class_org.apache.commons.math3.distribution.AbstractRealDistribution"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Fields inherited from class org.apache.commons.math3.distribution.<A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#random">random</A>, <A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#SOLVER_DEFAULT_ABSOLUTE_ACCURACY">SOLVER_DEFAULT_ABSOLUTE_ACCURACY</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<!-- ======== CONSTRUCTOR SUMMARY ======== -->

<A NAME="constructor_summary"><!-- --></A>
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<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Constructor Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution()">EmpiricalDistribution</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a new EmpiricalDistribution with the default bin count.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution(int)">EmpiricalDistribution</A></B>(int&nbsp;binCount)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a new EmpiricalDistribution with the specified bin count.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution(int, org.apache.commons.math3.random.RandomDataImpl)">EmpiricalDistribution</A></B>(int&nbsp;binCount,
                      <A HREF="../../../../../org/apache/commons/math3/random/RandomDataImpl.html" title="class in org.apache.commons.math3.random">RandomDataImpl</A>&nbsp;randomData)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Deprecated.</B>&nbsp;<I>As of 3.1. Please use <A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution(int, org.apache.commons.math3.random.RandomGenerator)"><CODE>EmpiricalDistribution(int,RandomGenerator)</CODE></A> instead.</I></TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution(int, org.apache.commons.math3.random.RandomGenerator)">EmpiricalDistribution</A></B>(int&nbsp;binCount,
                      <A HREF="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</A>&nbsp;generator)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a new EmpiricalDistribution with the specified bin count using the
 provided <A HREF="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random"><CODE>RandomGenerator</CODE></A> as the source of random data.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution(org.apache.commons.math3.random.RandomDataImpl)">EmpiricalDistribution</A></B>(<A HREF="../../../../../org/apache/commons/math3/random/RandomDataImpl.html" title="class in org.apache.commons.math3.random">RandomDataImpl</A>&nbsp;randomData)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Deprecated.</B>&nbsp;<I>As of 3.1. Please use <A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution(org.apache.commons.math3.random.RandomGenerator)"><CODE>EmpiricalDistribution(RandomGenerator)</CODE></A> instead.</I></TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution(org.apache.commons.math3.random.RandomGenerator)">EmpiricalDistribution</A></B>(<A HREF="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</A>&nbsp;generator)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a new EmpiricalDistribution with default bin count using the
 provided <A HREF="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random"><CODE>RandomGenerator</CODE></A> as the source of random data.</TD>
</TR>
</TABLE>
&nbsp;
<!-- ========== METHOD SUMMARY =========== -->

<A NAME="method_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Method Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#cumulativeProbability(double)">cumulativeProbability</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For a random variable <code>X</code> whose values are distributed according
 to this distribution, this method returns <code>P(X &lt;= x)</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#density(double)">density</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the probability density function (PDF) of this distribution
 evaluated at the specified point <code>x</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getBinCount()">getBinCount</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the number of bins.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="http://download.oracle.com/javase/6/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</A>&lt;<A HREF="../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive">SummaryStatistics</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getBinStats()">getBinStats</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a List of <A HREF="../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive"><CODE>SummaryStatistics</CODE></A> instances containing
 statistics describing the values in each of the bins.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getGeneratorUpperBounds()">getGeneratorUpperBounds</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a fresh copy of the array of upper bounds of the subintervals
 of [0,1] used in generating data from the empirical distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected &nbsp;<A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getKernel(org.apache.commons.math3.stat.descriptive.SummaryStatistics)">getKernel</A></B>(<A HREF="../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive">SummaryStatistics</A>&nbsp;bStats)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The within-bin smoothing kernel.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getNextValue()">getNextValue</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Generates a random value from this distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getNumericalMean()">getNumericalMean</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Use this method to get the numerical value of the mean of this
 distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getNumericalVariance()">getNumericalVariance</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Use this method to get the numerical value of the variance of this
 distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/stat/descriptive/StatisticalSummary.html" title="interface in org.apache.commons.math3.stat.descriptive">StatisticalSummary</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getSampleStats()">getSampleStats</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a <A HREF="../../../../../org/apache/commons/math3/stat/descriptive/StatisticalSummary.html" title="interface in org.apache.commons.math3.stat.descriptive"><CODE>StatisticalSummary</CODE></A> describing this distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getSupportLowerBound()">getSupportLowerBound</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Access the lower bound of the support.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getSupportUpperBound()">getSupportUpperBound</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Access the upper bound of the support.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getUpperBounds()">getUpperBounds</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a fresh copy of the array of upper bounds for the bins.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</A></B>(double&nbsp;p)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the quantile function of this distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#isLoaded()">isLoaded</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Property indicating whether or not the distribution has been loaded.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#isSupportConnected()">isSupportConnected</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Use this method to get information about whether the support is connected,
 i.e. whether all values between the lower and upper bound of the support
 are included in the support.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#isSupportLowerBoundInclusive()">isSupportLowerBoundInclusive</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Whether or not the lower bound of support is in the domain of the density
 function.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#isSupportUpperBoundInclusive()">isSupportUpperBoundInclusive</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Whether or not the upper bound of support is in the domain of the density
 function.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#load(double[])">load</A></B>(double[]&nbsp;in)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the empirical distribution from the provided
 array of numbers.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#load(java.io.File)">load</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/io/File.html?is-external=true" title="class or interface in java.io">File</A>&nbsp;file)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the empirical distribution from the input file.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#load(java.net.URL)">load</A></B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/net/URL.html?is-external=true" title="class or interface in java.net">URL</A>&nbsp;url)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Computes the empirical distribution using data read from a URL.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#probability(double)">probability</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For a random variable <code>X</code> whose values are distributed according
 to this distribution, this method returns <code>P(X = x)</code>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#reSeed(long)">reSeed</A></B>(long&nbsp;seed)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Reseeds the random number generator used by <A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getNextValue()"><CODE>getNextValue()</CODE></A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#reseedRandomGenerator(long)">reseedRandomGenerator</A></B>(long&nbsp;seed)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Reseed the random generator used to generate samples.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#sample()">sample</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Generate a random value sampled from this distribution.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_org.apache.commons.math3.distribution.AbstractRealDistribution"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math3.distribution.<A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#cumulativeProbability(double, double)">cumulativeProbability</A>, <A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#getSolverAbsoluteAccuracy()">getSolverAbsoluteAccuracy</A>, <A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#probability(double, double)">probability</A>, <A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#sample(int)">sample</A></CODE></TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<P>

<!-- ============ FIELD DETAIL =========== -->

<A NAME="field_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Field Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="DEFAULT_BIN_COUNT"><!-- --></A><H3>
DEFAULT_BIN_COUNT</H3>
<PRE>
public static final int <B>DEFAULT_BIN_COUNT</B></PRE>
<DL>
<DD>Default bin count
<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../../../../../constant-values.html#org.apache.commons.math3.random.EmpiricalDistribution.DEFAULT_BIN_COUNT">Constant Field Values</A></DL>
</DL>
<HR>

<A NAME="randomData"><!-- --></A><H3>
randomData</H3>
<PRE>
protected final <A HREF="../../../../../org/apache/commons/math3/random/RandomDataGenerator.html" title="class in org.apache.commons.math3.random">RandomDataGenerator</A> <B>randomData</B></PRE>
<DL>
<DD>RandomDataGenerator instance to use in repeated calls to getNext()
<P>
<DL>
</DL>
</DL>

<!-- ========= CONSTRUCTOR DETAIL ======== -->

<A NAME="constructor_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Constructor Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="EmpiricalDistribution()"><!-- --></A><H3>
EmpiricalDistribution</H3>
<PRE>
public <B>EmpiricalDistribution</B>()</PRE>
<DL>
<DD>Creates a new EmpiricalDistribution with the default bin count.
<P>
</DL>
<HR>

<A NAME="EmpiricalDistribution(int)"><!-- --></A><H3>
EmpiricalDistribution</H3>
<PRE>
public <B>EmpiricalDistribution</B>(int&nbsp;binCount)</PRE>
<DL>
<DD>Creates a new EmpiricalDistribution with the specified bin count.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>binCount</CODE> - number of bins</DL>
</DL>
<HR>

<A NAME="EmpiricalDistribution(int, org.apache.commons.math3.random.RandomGenerator)"><!-- --></A><H3>
EmpiricalDistribution</H3>
<PRE>
public <B>EmpiricalDistribution</B>(int&nbsp;binCount,
                             <A HREF="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</A>&nbsp;generator)</PRE>
<DL>
<DD>Creates a new EmpiricalDistribution with the specified bin count using the
 provided <A HREF="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random"><CODE>RandomGenerator</CODE></A> as the source of random data.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>binCount</CODE> - number of bins<DD><CODE>generator</CODE> - random data generator (may be null, resulting in default JDK generator)<DT><B>Since:</B></DT>
  <DD>3.0</DD>
</DL>
</DL>
<HR>

<A NAME="EmpiricalDistribution(org.apache.commons.math3.random.RandomGenerator)"><!-- --></A><H3>
EmpiricalDistribution</H3>
<PRE>
public <B>EmpiricalDistribution</B>(<A HREF="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</A>&nbsp;generator)</PRE>
<DL>
<DD>Creates a new EmpiricalDistribution with default bin count using the
 provided <A HREF="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random"><CODE>RandomGenerator</CODE></A> as the source of random data.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>generator</CODE> - random data generator (may be null, resulting in default JDK generator)<DT><B>Since:</B></DT>
  <DD>3.0</DD>
</DL>
</DL>
<HR>

<A NAME="EmpiricalDistribution(int, org.apache.commons.math3.random.RandomDataImpl)"><!-- --></A><H3>
EmpiricalDistribution</H3>
<PRE>
<FONT SIZE="-1"><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</A>
</FONT>public <B>EmpiricalDistribution</B>(int&nbsp;binCount,
                                        <A HREF="../../../../../org/apache/commons/math3/random/RandomDataImpl.html" title="class in org.apache.commons.math3.random">RandomDataImpl</A>&nbsp;randomData)</PRE>
<DL>
<DD><B>Deprecated.</B>&nbsp;<I>As of 3.1. Please use <A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution(int, org.apache.commons.math3.random.RandomGenerator)"><CODE>EmpiricalDistribution(int,RandomGenerator)</CODE></A> instead.</I>
<P>
<DD>Creates a new EmpiricalDistribution with the specified bin count using the
 provided <A HREF="../../../../../org/apache/commons/math3/random/RandomDataImpl.html" title="class in org.apache.commons.math3.random"><CODE>RandomDataImpl</CODE></A> instance as the source of random data.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>binCount</CODE> - number of bins<DD><CODE>randomData</CODE> - random data generator (may be null, resulting in default JDK generator)<DT><B>Since:</B></DT>
  <DD>3.0</DD>
</DL>
</DL>
<HR>

<A NAME="EmpiricalDistribution(org.apache.commons.math3.random.RandomDataImpl)"><!-- --></A><H3>
EmpiricalDistribution</H3>
<PRE>
<FONT SIZE="-1"><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</A>
</FONT>public <B>EmpiricalDistribution</B>(<A HREF="../../../../../org/apache/commons/math3/random/RandomDataImpl.html" title="class in org.apache.commons.math3.random">RandomDataImpl</A>&nbsp;randomData)</PRE>
<DL>
<DD><B>Deprecated.</B>&nbsp;<I>As of 3.1. Please use <A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#EmpiricalDistribution(org.apache.commons.math3.random.RandomGenerator)"><CODE>EmpiricalDistribution(RandomGenerator)</CODE></A> instead.</I>
<P>
<DD>Creates a new EmpiricalDistribution with default bin count using the
 provided <A HREF="../../../../../org/apache/commons/math3/random/RandomDataImpl.html" title="class in org.apache.commons.math3.random"><CODE>RandomDataImpl</CODE></A> as the source of random data.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>randomData</CODE> - random data generator (may be null, resulting in default JDK generator)<DT><B>Since:</B></DT>
  <DD>3.0</DD>
</DL>
</DL>

<!-- ============ METHOD DETAIL ========== -->

<A NAME="method_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Method Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="load(double[])"><!-- --></A><H3>
load</H3>
<PRE>
public void <B>load</B>(double[]&nbsp;in)
          throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Computes the empirical distribution from the provided
 array of numbers.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>in</CODE> - the input data array
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if in is null</DL>
</DD>
</DL>
<HR>

<A NAME="load(java.net.URL)"><!-- --></A><H3>
load</H3>
<PRE>
public void <B>load</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/net/URL.html?is-external=true" title="class or interface in java.net">URL</A>&nbsp;url)
          throws <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A>,
                 <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                 <A HREF="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</A></PRE>
<DL>
<DD>Computes the empirical distribution using data read from a URL.

 <p>The input file <i>must</i> be an ASCII text file containing one
 valid numeric entry per line.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>url</CODE> - url of the input file
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></CODE> - if an IO error occurs
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if url is null
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</A></CODE> - if URL contains no data</DL>
</DD>
</DL>
<HR>

<A NAME="load(java.io.File)"><!-- --></A><H3>
load</H3>
<PRE>
public void <B>load</B>(<A HREF="http://download.oracle.com/javase/6/docs/api/java/io/File.html?is-external=true" title="class or interface in java.io">File</A>&nbsp;file)
          throws <A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A>,
                 <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></PRE>
<DL>
<DD>Computes the empirical distribution from the input file.

 <p>The input file <i>must</i> be an ASCII text file containing one
 valid numeric entry per line.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>file</CODE> - the input file
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/io/IOException.html?is-external=true" title="class or interface in java.io">IOException</A></CODE> - if an IO error occurs
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if file is null</DL>
</DD>
</DL>
<HR>

<A NAME="getNextValue()"><!-- --></A><H3>
getNextValue</H3>
<PRE>
public double <B>getNextValue</B>()
                    throws <A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</A></PRE>
<DL>
<DD>Generates a random value from this distribution.
 <strong>Preconditions:</strong><ul>
 <li>the distribution must be loaded before invoking this method</li></ul>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the random value.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MathIllegalStateException.html" title="class in org.apache.commons.math3.exception">MathIllegalStateException</A></CODE> - if the distribution has not been loaded</DL>
</DD>
</DL>
<HR>

<A NAME="getSampleStats()"><!-- --></A><H3>
getSampleStats</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/stat/descriptive/StatisticalSummary.html" title="interface in org.apache.commons.math3.stat.descriptive">StatisticalSummary</A> <B>getSampleStats</B>()</PRE>
<DL>
<DD>Returns a <A HREF="../../../../../org/apache/commons/math3/stat/descriptive/StatisticalSummary.html" title="interface in org.apache.commons.math3.stat.descriptive"><CODE>StatisticalSummary</CODE></A> describing this distribution.
 <strong>Preconditions:</strong><ul>
 <li>the distribution must be loaded before invoking this method</li></ul>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the sample statistics
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/IllegalStateException.html?is-external=true" title="class or interface in java.lang">IllegalStateException</A></CODE> - if the distribution has not been loaded</DL>
</DD>
</DL>
<HR>

<A NAME="getBinCount()"><!-- --></A><H3>
getBinCount</H3>
<PRE>
public int <B>getBinCount</B>()</PRE>
<DL>
<DD>Returns the number of bins.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the number of bins.</DL>
</DD>
</DL>
<HR>

<A NAME="getBinStats()"><!-- --></A><H3>
getBinStats</H3>
<PRE>
public <A HREF="http://download.oracle.com/javase/6/docs/api/java/util/List.html?is-external=true" title="class or interface in java.util">List</A>&lt;<A HREF="../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive">SummaryStatistics</A>&gt; <B>getBinStats</B>()</PRE>
<DL>
<DD>Returns a List of <A HREF="../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive"><CODE>SummaryStatistics</CODE></A> instances containing
 statistics describing the values in each of the bins.  The list is
 indexed on the bin number.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>List of bin statistics.</DL>
</DD>
</DL>
<HR>

<A NAME="getUpperBounds()"><!-- --></A><H3>
getUpperBounds</H3>
<PRE>
public double[] <B>getUpperBounds</B>()</PRE>
<DL>
<DD><p>Returns a fresh copy of the array of upper bounds for the bins.
 Bins are: <br/>
 [min,upperBounds[0]],(upperBounds[0],upperBounds[1]],...,
  (upperBounds[binCount-2], upperBounds[binCount-1] = max].</p>

 <p>Note: In versions 1.0-2.0 of commons-math, this method
 incorrectly returned the array of probability generator upper
 bounds now returned by <A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getGeneratorUpperBounds()"><CODE>getGeneratorUpperBounds()</CODE></A>.</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>array of bin upper bounds<DT><B>Since:</B></DT>
  <DD>2.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="getGeneratorUpperBounds()"><!-- --></A><H3>
getGeneratorUpperBounds</H3>
<PRE>
public double[] <B>getGeneratorUpperBounds</B>()</PRE>
<DL>
<DD><p>Returns a fresh copy of the array of upper bounds of the subintervals
 of [0,1] used in generating data from the empirical distribution.
 Subintervals correspond to bins with lengths proportional to bin counts.</p>

 <p>In versions 1.0-2.0 of commons-math, this array was (incorrectly) returned
 by <A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getUpperBounds()"><CODE>getUpperBounds()</CODE></A>.</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>array of upper bounds of subintervals used in data generation<DT><B>Since:</B></DT>
  <DD>2.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="isLoaded()"><!-- --></A><H3>
isLoaded</H3>
<PRE>
public boolean <B>isLoaded</B>()</PRE>
<DL>
<DD>Property indicating whether or not the distribution has been loaded.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>true if the distribution has been loaded</DL>
</DD>
</DL>
<HR>

<A NAME="reSeed(long)"><!-- --></A><H3>
reSeed</H3>
<PRE>
public void <B>reSeed</B>(long&nbsp;seed)</PRE>
<DL>
<DD>Reseeds the random number generator used by <A HREF="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html#getNextValue()"><CODE>getNextValue()</CODE></A>.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>seed</CODE> - random generator seed<DT><B>Since:</B></DT>
  <DD>3.0</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="probability(double)"><!-- --></A><H3>
probability</H3>
<PRE>
public double <B>probability</B>(double&nbsp;x)</PRE>
<DL>
<DD>For a random variable <code>X</code> whose values are distributed according
 to this distribution, this method returns <code>P(X = x)</code>. In other
 words, this method represents the probability mass function (PMF)
 for the distribution.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#probability(double)">probability</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</A></CODE><DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#probability(double)">probability</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the point at which the PMF is evaluated
<DT><B>Returns:</B><DD>zero.<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="density(double)"><!-- --></A><H3>
density</H3>
<PRE>
public double <B>density</B>(double&nbsp;x)</PRE>
<DL>
<DD>Returns the probability density function (PDF) of this distribution
 evaluated at the specified point <code>x</code>. In general, the PDF is
 the derivative of the <A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double)"><CODE>CDF</CODE></A>.
 If the derivative does not exist at <code>x</code>, then an appropriate
 replacement should be returned, e.g. <code>Double.POSITIVE_INFINITY</code>,
 <code>Double.NaN</code>, or  the limit inferior or limit superior of the
 difference quotient.

 <p>Returns the kernel density normalized so that its integral over each bin
 equals the bin mass.</p>

 <p>Algorithm description: <ol>
 <li>Find the bin B that x belongs to.</li>
 <li>Compute K(B) = the mass of B with respect to the within-bin kernel (i.e., the
 integral of the kernel density over B).</li>
 <li>Return k(x) * P(B) / K(B), where k is the within-bin kernel density
 and P(B) is the mass of B.</li></ol></p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the point at which the PDF is evaluated
<DT><B>Returns:</B><DD>the value of the probability density function at point <code>x</code><DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="cumulativeProbability(double)"><!-- --></A><H3>
cumulativeProbability</H3>
<PRE>
public double <B>cumulativeProbability</B>(double&nbsp;x)</PRE>
<DL>
<DD>For a random variable <code>X</code> whose values are distributed according
 to this distribution, this method returns <code>P(X &lt;= x)</code>. In other
 words, this method represents the (cumulative) distribution function
 (CDF) for this distribution.

 <p>Algorithm description:<ol>
 <li>Find the bin B that x belongs to.</li>
 <li>Compute P(B) = the mass of B and P(B-) = the combined mass of the bins below B.</li>
 <li>Compute K(B) = the probability mass of B with respect to the within-bin kernel
 and K(B-) = the kernel distribution evaluated at the lower endpoint of B</li>
 <li>Return P(B-) + P(B) * [K(x) - K(B-)] / K(B) where
 K(x) is the within-bin kernel distribution function evaluated at x.</li></ol></p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the point at which the CDF is evaluated
<DT><B>Returns:</B><DD>the probability that a random variable with this
 distribution takes a value less than or equal to <code>x</code><DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="inverseCumulativeProbability(double)"><!-- --></A><H3>
inverseCumulativeProbability</H3>
<PRE>
public double <B>inverseCumulativeProbability</B>(double&nbsp;p)
                                    throws <A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></PRE>
<DL>
<DD>Computes the quantile function of this distribution. For a random
 variable <code>X</code> distributed according to this distribution, the
 returned value is
 <ul>
 <li><code>inf{x in R | P(X<=x) >= p}</code> for <code>0 &lt; p &lt;= 1</code>,</li>
 <li><code>inf{x in R | P(X<=x) > 0}</code> for <code>p = 0</code>.</li>
 </ul>

 The default implementation returns
 <ul>
 <li><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#getSupportLowerBound()"><CODE>RealDistribution.getSupportLowerBound()</CODE></A> for <code>p = 0</code>,</li>
 <li><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#getSupportUpperBound()"><CODE>RealDistribution.getSupportUpperBound()</CODE></A> for <code>p = 1</code>.</li>
 </ul>

 <p>Algorithm description:<ol>
 <li>Find the smallest i such that the sum of the masses of the bins
  through i is at least p.</li>
 <li>
   Let K be the within-bin kernel distribution for bin i.</br>
   Let K(B) be the mass of B under K. <br/>
   Let K(B-) be K evaluated at the lower endpoint of B (the combined
   mass of the bins below B under K).<br/>
   Let P(B) be the probability of bin i.<br/>
   Let P(B-) be the sum of the bin masses below bin i. <br/>
   Let pCrit = p - P(B-)<br/>
 <li>Return the inverse of K evaluated at <br/>
    K(B-) + pCrit * K(B) / P(B) </li>
  </ol></p>
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</A></CODE><DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>p</CODE> - the cumulative probability
<DT><B>Returns:</B><DD>the smallest <code>p</code>-quantile of this distribution
 (largest 0-quantile for <code>p = 0</code>)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</A></CODE> - if <code>p &lt; 0</code> or <code>p &gt; 1</code><DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="getNumericalMean()"><!-- --></A><H3>
getNumericalMean</H3>
<PRE>
public double <B>getNumericalMean</B>()</PRE>
<DL>
<DD>Use this method to get the numerical value of the mean of this
 distribution.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the mean or <code>Double.NaN</code> if it is not defined<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="getNumericalVariance()"><!-- --></A><H3>
getNumericalVariance</H3>
<PRE>
public double <B>getNumericalVariance</B>()</PRE>
<DL>
<DD>Use this method to get the numerical value of the variance of this
 distribution.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the variance (possibly <code>Double.POSITIVE_INFINITY</code> as
 for certain cases in <A HREF="../../../../../org/apache/commons/math3/distribution/TDistribution.html" title="class in org.apache.commons.math3.distribution"><CODE>TDistribution</CODE></A>) or <code>Double.NaN</code> if it
 is not defined<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="getSupportLowerBound()"><!-- --></A><H3>
getSupportLowerBound</H3>
<PRE>
public double <B>getSupportLowerBound</B>()</PRE>
<DL>
<DD>Access the lower bound of the support. This method must return the same
 value as <code>inverseCumulativeProbability(0)</code>. In other words, this
 method must return
 <p><code>inf {x in R | P(X <= x) > 0}</code>.</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>lower bound of the support (might be
 <code>Double.NEGATIVE_INFINITY</code>)<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="getSupportUpperBound()"><!-- --></A><H3>
getSupportUpperBound</H3>
<PRE>
public double <B>getSupportUpperBound</B>()</PRE>
<DL>
<DD>Access the upper bound of the support. This method must return the same
 value as <code>inverseCumulativeProbability(1)</code>. In other words, this
 method must return
 <p><code>inf {x in R | P(X <= x) = 1}</code>.</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>upper bound of the support (might be
 <code>Double.POSITIVE_INFINITY</code>)<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="isSupportLowerBoundInclusive()"><!-- --></A><H3>
isSupportLowerBoundInclusive</H3>
<PRE>
public boolean <B>isSupportLowerBoundInclusive</B>()</PRE>
<DL>
<DD>Whether or not the lower bound of support is in the domain of the density
 function.  Returns true iff <code>getSupporLowerBound()</code> is finite and
 <code>density(getSupportLowerBound())</code> returns a non-NaN, non-infinite
 value.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>true if the lower bound of support is finite and the density
 function returns a non-NaN, non-infinite value there<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="isSupportUpperBoundInclusive()"><!-- --></A><H3>
isSupportUpperBoundInclusive</H3>
<PRE>
public boolean <B>isSupportUpperBoundInclusive</B>()</PRE>
<DL>
<DD>Whether or not the upper bound of support is in the domain of the density
 function.  Returns true iff <code>getSupportUpperBound()</code> is finite and
 <code>density(getSupportUpperBound())</code> returns a non-NaN, non-infinite
 value.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>true if the upper bound of support is finite and the density
 function returns a non-NaN, non-infinite value there<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="isSupportConnected()"><!-- --></A><H3>
isSupportConnected</H3>
<PRE>
public boolean <B>isSupportConnected</B>()</PRE>
<DL>
<DD>Use this method to get information about whether the support is connected,
 i.e. whether all values between the lower and upper bound of the support
 are included in the support.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>whether the support is connected or not<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="sample()"><!-- --></A><H3>
sample</H3>
<PRE>
public double <B>sample</B>()</PRE>
<DL>
<DD>Generate a random value sampled from this distribution.

 The default implementation uses the
 <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling">
 inversion method.
 </a>
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#sample()">sample</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</A></CODE><DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#sample()">sample</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</A></CODE></DL>
</DD>
<DD><DL>

<DT><B>Returns:</B><DD>a random value.<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="reseedRandomGenerator(long)"><!-- --></A><H3>
reseedRandomGenerator</H3>
<PRE>
public void <B>reseedRandomGenerator</B>(long&nbsp;seed)</PRE>
<DL>
<DD>Reseed the random generator used to generate samples.
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#reseedRandomGenerator(long)">reseedRandomGenerator</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</A></CODE><DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#reseedRandomGenerator(long)">reseedRandomGenerator</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>seed</CODE> - the new seed<DT><B>Since:</B></DT>
  <DD>3.1</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="getKernel(org.apache.commons.math3.stat.descriptive.SummaryStatistics)"><!-- --></A><H3>
getKernel</H3>
<PRE>
protected <A HREF="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</A> <B>getKernel</B>(<A HREF="../../../../../org/apache/commons/math3/stat/descriptive/SummaryStatistics.html" title="class in org.apache.commons.math3.stat.descriptive">SummaryStatistics</A>&nbsp;bStats)</PRE>
<DL>
<DD>The within-bin smoothing kernel.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>bStats</CODE> - summary statistics for the bin
<DT><B>Returns:</B><DD>within-bin kernel parameterized by bStats</DL>
</DD>
</DL>
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